Generating entanglement and squeezed states of nuclear spins in quantum dots

Non-Gaussian Dynamics of Quantum Fluctuations and Mean-Field Limit in Open Quantum Central Spin Systems

Central spin systems, in which a central spin is singled out and interacts nonlocally with several bath spins, are paradigmatic models for nitrogen-vacancy centers and quantum dots. They show complex emergent dynamics and stationary phenomena which, despite the collective nature of their interaction, are still largely not understood. Here, we derive exact results on the emergent behavior of open quantum central spin systems. The latter crucially depends on the scaling of the interaction strength with the bath size. For scalings with the inverse square root of the bath size (typical of one-to-many interactions), the system behaves, in the thermodynamic limit, as an open quantum Jaynes-Cummings model, whose bosonic mode encodes the quantum fluctuations of the bath spins. In this case, non-Gaussian correlations are dynamically generated and persist at stationarity. For scalings with the inverse bath size, the emergent dynamics is instead of mean-field type. Our Letter provides a fundamental understanding of the different dynamical regimes of central spin systems and a simple theory for efficiently exploring their nonequilibrium behavior. Our findings may become relevant for developing fully quantum descriptions of many-body solid-state devices and their applications.

Electronic Quantum Materials Simulated with Artificial Model Lattices

The band structure and electronic properties of a material are defined by the sort of elements, the atomic registry in the crystal, the dimensions, the presence of spin–orbit coupling, and the electronic interactions. In natural crystals, the interplay of these factors is difficult to unravel, since it is usually not possible to vary one of these factors in an independent way, keeping the others constant. In other words, a complete understanding of complex electronic materials remains challenging to date. The geometry of two- and one-dimensional crystals can be mimicked in artificial lattices. Moreover, geometries that do not exist in nature can be created for the sake of further insight. Such engineered artificial lattices can be better controlled and fine-tuned than natural crystals. This makes it easier to vary the lattice geometry, dimensions, spin–orbit coupling, and interactions independently from each other. Thus, engineering and characterization of artificial lattices can provide unique insights. In this Review, we focus on artificial lattices that are built atom-by-atom on atomically flat metals, using atomic manipulation in a scanning tunneling microscope. Cryogenic scanning tunneling microscopy allows for consecutive creation, microscopic characterization, and band-structure analysis by tunneling spectroscopy, amounting in the analogue quantum simulation of a given lattice type. We first review the physical elements of this method. We then discuss the creation and characterization of artificial atoms and molecules. For the lattices, we review works on honeycomb and Lieb lattices and lattices that result in crystalline topological insulators, such as the Kekulé and “breathing” kagome lattice. Geometric but nonperiodic structures such as electronic quasi-crystals and fractals are discussed as well. Finally, we consider the option to transfer the knowledge gained back to real materials, engineered by geometric patterning of semiconductor quantum wells.

Nuclear Spin Dynamics, Noise, Squeezing, and Entanglement in Box Model

We obtain a compact analytical solution for the nonlinear equation for the nuclear spin dynamics in the central spin box model in the limit of many nuclear spins. The total nuclear spin component along the external magnetic field is conserved and the two perpendicular components precess or oscillate depending on the electron spin polarization, with the frequency, determined by the nuclear spin polarization. As applications of our solution, we calculate the nuclear spin noise spectrum and describe the effects of nuclear spin squeezing and many body entanglement in the absence of a system excitation.

Protecting Spin Coherence in a Tunable Heisenberg Model

Using an ensemble of atoms in an optical cavity, we engineer a family of nonlocal Heisenberg Hamiltonians with continuously tunable anisotropy of the spin-spin couplings. We thus gain access to a rich phase diagram, including a paramagnetic-to-ferromagnetic Ising phase transition that manifests as a diverging magnetic susceptibility at the critical point. The susceptibility displays a symmetry between Ising interactions and XY (spin-exchange) interactions of the opposite sign, which is indicative of the spatially extended atomic system behaving as a single collective spin. Images of the magnetization dynamics show that spin-exchange interactions protect the coherence of the collective spin, even against inhomogeneous fields that completely dephase the noninteracting and Ising systems. Our results underscore prospects for harnessing spin-exchange interactions to enhance the robustness of spin squeezing protocols.

Generation of multiqubit steady-state quantum correlation by squeezed-reservoir engineering

Stationary quantum correlation among two-level systems (TLSs) in steady state is one of unique resources for applications in quantum information processing. Here we propose a scheme to generate such quantum correlation among the TLSs inside a lossy cavity. It is found that, by applying a broadband squeezed laser acting as a squeezed-vacuum reservoir to the cavity, a stable quantum correlation of the TLSs can be generated. By adiabatically eliminating the cavity field, we derive a reduced master equation of the TLSs in the bad-cavity limit. We show that the generated quantum correlation is essentially determined by the squeezing features transferred from the squeezed-vacuum reservoir via the cavity field as a quantum bus. We study the effect of the system parameters, such as the squeezing, the detuning, the coupling strength, and the decay rate of the TLSs, on the performance of the scheme. The feasibility of our proposal is supported by the application of currently available experimental techniques.

Improving a Solid-State Qubit through an Engineered Mesoscopic Environment

A controlled quantum system can alter its environment by feedback, leading to reduced-entropy states of the environment and to improved system coherence. Here, using a quantum-dot electron spin as a control and probe, we prepare the quantum-dot nuclei under the feedback of coherent population trapping and observe their evolution from a thermal to a reduced-entropy state, with the immediate consequence of extended qubit coherence. Via Ramsey interferometry on the electron spin, we directly access the nuclear distribution following its preparation and measure the emergence and decay of correlations within the nuclear ensemble. Under optimal feedback, the inhomogeneous dephasing time of the electron, T_{2}^{*}, is extended by an order of magnitude to 39 ns. Our results can be readily exploited in quantum information protocols utilizing spin-photon entanglement and represent a step towards creating quantum many-body states in a mesoscopic nuclear-spin ensemble.

Approaching the Heisenberg Limit without Single-Particle Detection

We propose an approach to quantum phase estimation that can attain precision near the Heisenberg limit without requiring single-particle-resolved state detection. We show that the "one-axis twisting" interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Applying this interaction-based readout to oversqueezed, non-Gaussian states yields a Heisenberg scaling in phase sensitivity, which persists in the presence of detection noise as large as the quantum projection noise of an unentangled ensemble. Even in dissipative implementations-e.g., employing light-mediated interactions in an optical cavity or Rydberg dressing-the method significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit.

Spin squeezing in a quadrupolar nuclei NMR system

We have produced and characterized spin-squeezed states at a temperature of 26 °C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on 133Cs nuclei of spin I=7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I+1=8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.

Steady-state entanglement in the nuclear spin dynamics of a double quantum dot

We propose a scheme for the deterministic generation of steady-state entanglement between the two nuclear spin ensembles in an electrically defined double quantum dot. Because of quantum interference in the collective coupling to the electronic degrees of freedom, the nuclear system is actively driven into a two-mode squeezedlike target state. The entanglement buildup is accompanied by a self-polarization of the nuclear spins towards large Overhauser field gradients. Moreover, the feedback between the electronic and nuclear dynamics leads to multistability and criticality in the steady-state solutions.

Nuclear spin effects in semiconductor quantum dots

The interaction of an electronic spin with its nuclear environment, an issue known as the central spin problem, has been the subject of considerable attention due to its relevance for spin-based quantum computation using semiconductor quantum dots. Independent control of the nuclear spin bath using nuclear magnetic resonance techniques and dynamic nuclear polarization using the central spin itself offer unique possibilities for manipulating the nuclear bath with significant consequences for the coherence and controlled manipulation of the central spin. Here we review some of the recent optical and transport experiments that have explored this central spin problem using semiconductor quantum dots. We focus on the interaction between 10(4)-10(6) nuclear spins and a spin of a single electron or valence-band hole. We also review the experimental techniques as well as the key theoretical ideas and the implications for quantum information science.

Large nuclear spin polarization in gate-defined quantum dots using a single-domain nanomagnet

The electron-nuclei (hyperfine) interaction is central to spin qubits in solid state systems. It can be a severe decoherence source but also allows dynamic access to the nuclear spin states. We study a double quantum dot exposed to an on-chip single-domain nanomagnet and show that its inhomogeneous magnetic field crucially modifies the complex nuclear spin dynamics such that the Overhauser field tends to compensate external magnetic fields. This turns out to be beneficial for polarizing the nuclear spin ensemble. We reach a nuclear spin polarization of ≃50%, unrivaled in lateral dots, and explain our manipulation technique using a comprehensive rate equation model.

Phonon-induced spin-spin interactions in diamond nanostructures: application to spin squeezing

We propose and analyze a novel mechanism for long-range spin-spin interactions in diamond nanostructures. The interactions between electronic spins, associated with nitrogen-vacancy centers in diamond, are mediated by their coupling via strain to the vibrational mode of a diamond mechanical nanoresonator. This coupling results in phonon-mediated effective spin-spin interactions that can be used to generate squeezed states of a spin ensemble. We show that spin dephasing and relaxation can be largely suppressed, allowing for substantial spin squeezing under realistic experimental conditions. Our approach has implications for spin-ensemble magnetometry, as well as phonon-mediated quantum information processing with spin qubits.

Optical pump-probe detection of manganese hyperfine beats in (Cd,Mn)Te crystals

Optical pump-probe experiments reveal spin beats of manganese ions in (Cd,Mn)Te, due to hyperfine and crystal fields. At "magic" orientations of the magnetic field, the effect of local crystal field is strongly suppressed. In this case, the spin precession of Mn(2+) embedded in the lattice approaches the precession expected for the free ion. Following optical excitation, regular spin pulses show up, revealing the one-to-one correspondence between precession frequency and Mn(2+) nuclear spin state. The period of the spin pulses accurately determines the hyperfine constant |A|=705  neV. The manganese spin coherence time up to T(2)(Mn)≃15  ns is measured for a manganese concentration x=0.0011.

Controlling the quantum dynamics of a mesoscopic spin bath in diamond

Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Here, we demonstrate quantum control of a mesoscopic spin bath in diamond at room temperature that is composed of electron spins of substitutional nitrogen impurities. The resulting spin bath dynamics are probed using a single nitrogen-vacancy (NV) centre electron spin as a magnetic field sensor. We exploit the spin bath control to dynamically suppress dephasing of the NV spin by the spin bath. Furthermore, by combining spin bath control with dynamical decoupling, we directly measure the coherence and temporal correlations of different groups of bath spins. These results uncover a new arena for fundamental studies on decoherence and enable novel avenues for spin-based magnetometry and quantum information processing.

Fast control of nuclear spin polarization in an optically pumped single quantum dot

Highly polarized nuclear spins within a semiconductor quantum dot induce effective magnetic (Overhauser) fields of up to several Tesla acting on the electron spin, or up to a few hundred mT for the hole spin. Recently this has been recognized as a resource for intrinsic control of quantum-dot-based spin quantum bits. However, only static long-lived Overhauser fields could be used. Here we demonstrate fast redirection on the microsecond timescale of Overhauser fields on the order of 0.5 T experienced by a single electron spin in an optically pumped GaAs quantum dot. This has been achieved using coherent control of an ensemble of 10(5) optically polarized nuclear spins by sequences of short radiofrequency pulses. These results open the way to a new class of experiments using radiofrequency techniques to achieve highly correlated nuclear spins in quantum dots, such as adiabatic demagnetization in the rotating frame leading to sub-μK nuclear spin temperatures, rapid adiabatic passage, and spin squeezing.